Course Name Code Semester T+U Hours Credit ECTS
Differential Equations MAT 202 4 4 + 0 4 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Bachelor's Degree
Course Type Compulsory
Course Coordinator Prof.Dr. ŞEVKET GÜR
Course Lecturers Prof.Dr. UĞUR ARİFOĞLU, Doç.Dr. NEZAKET PARLAK, Doç.Dr. ZEKERİYA PARLAK, Prof.Dr. EKREM BÜYÜKKAYA, Dr.Öğr.Üyesi ALPER KİRAZ, Prof.Dr. ÖMER FARUK GÖZÜKIZIL, Prof.Dr. ŞEVKET GÜR, Prof.Dr. METİN YAMAN, Doç.Dr. ÜNAL UYSAL, Dr.Öğr.Üyesi ABDULLAH HULUSİ KÖKÇAM,
Course Assistants
Course Category Available Basic Education in the Field
Course Objective

The general pourpose of this course is to provide an understanding of ordinary differential equations (ODEs), and to give methods for solving them. Because differential equations express relationships between changing quantities, this material is applicable to many fields, and is essential for students of engineering and physical sciences.

Course Content

Basic concepts and classifying differential equations, variable separated differential equations, Homogenous differential equations, exact differential equation, Integrator method, First order linear differential equations, finding solution for a linearized differential equations, Bernoulli differential equations, Ricatti differential equations, separation of variables, First order high degree differential equations, Singular solution of differential equations. Clairaut differential equation, Lagrange differential equation, Numeric solutions of differential equations, Taylor series method, Picard iteration method, Runge-Kutta method, High order linear differential equations, Criteria for linear independence, Solution of high order, one side, constant coefficient linear differential  equation. Undetermined coefficients method, Exchange of Lagrange constants method. General solution of Euler differential equations. Decreasing the degree of a differential equation. Solution of constant coefficient differential equation with operator method. Linear differential equations. State equations. Solutions of differential equations with one side. Solution of differential equation systems with Eigen characteristic equation. Laplace conversion. Laplace transformation of derivatives. Methods of separation to basic fractions. Reverse Laplace transformation. Solution of constant coefficient linear differential equations with Laplace transformation. Convolution. Application of Convolution theorem to integral equations. Laplace transformation of periodic functions. Solution of partial derivative differential equations with Laplace transformation. Laplace transformation of step functions. Laplace transformation of impulse functions. Solution of differential equations with series. Bessel functions. Gamma function.

# Course Learning Outcomes Teaching Methods Assessment Methods
1 Understands the terminology about the differential equations. Lecture, Question-Answer, Discussion, Drilland Practice, Testing, Homework,
2 Verify that a given function is solution of a differential equation Drilland Practice, Question-Answer, Lecture, Homework, Testing,
3 Solve problems of ordinary differential equations and system of differential equations Problem Solving, Drilland Practice, Discussion, Question-Answer, Lecture, Testing, Homework,
4 Apply knowledge of differential equations in order to solve real-world engineering problems Problem Solving, Drilland Practice, Discussion, Question-Answer, Lecture, Homework, Testing,
5 Problem Solving, Drilland Practice, Discussion, Question-Answer, Lecture, Homework, Testing,
6 Problem Solving, Drilland Practice, Discussion, Question-Answer, Lecture, Homework, Testing,
7 Problem Solving, Drilland Practice, Discussion, Question-Answer, Lecture, Homework, Testing,
8 Problem Solving, Drilland Practice, Discussion, Question-Answer, Lecture, Homework, Testing,
Week Course Topics Preliminary Preparation
1 Basic Concepts and Classifying Differential Equations. Obtaining differential equations. Separable differential equations. Engineering applications.
2 Homogeneous functions, homogenous differential equations. Exact differential equations and engineering applications.
3 Non-Linear First Order linear Equations. Integration factor method. Change of variables method. Change of Lagrange variables method. Engineering Applications.
4 Solution of differential equations by changing to the linear form. Bernoulli differential equation. Ricatti differential equation. Engineering applications.
5 Second-Order Linear Equations: Linear Independence, Homogeneous Equations with Constant Coefficients
6 General solution of high order one sided, constant coefficient linear differential equations. Criteria of linear independence. Wronski determinant. Engineering applications.
7 General solution of high order two sided, constant coefficient linear differential equations. Undetermined coefficients method. LSD method. Engineering applications.
8 Euler differential equations. Decreasing the degree of a differential equation. Solution of constant coefficient differential equation with operator method.
9 Mid-Term Exam
10 Introduction to differential equation systems. Linear differential equation systems. Solution of one sided linear differential equation systems. Eigen characteristic equation. Engineering applications.
11 Solution of one sided linear differential equations. Undetermined coefficients method. Change of Lagrange constants method. Engineering applications.
12 Laplace transformation, Laplace transformation of derivati.ve. Reverse Laplace transformation. Separation of basic fractions. Engineering applications.
13 Laplace Transform Method
14 Solution of differential equations with series. Bessel functions. Gamma function.
Resources
Course Notes <p>&Ccedil;engel, Y. A. ve Palm, W. J. (T&uuml;rk&ccedil;esi: Tahsin Engin), 2012, M&uuml;hendisler ve Fen Bilimciler İ&ccedil;in Diferansiyel Denklemler, G&uuml;ven Kitabevi, İzmir.</p>
Course Resources

1. Türker, E. S. ve Başarır, M., 2003, Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Kitabevi, Sakarya.
2. Bronson, R.,1993, Differantial Equations, Schaum´s Outlines, Nobel Kitabevi, Ankara.
3. Edwards, C. H.ve Penney, D. E., (Türkçesi: Ömer Akın) 2008, Diferansiyel Denklemler ve Sınır Değer Problemleri,Palme Yayıncılık.

Order Program Outcomes Level of Contribution
1 2 3 4 5
1 To have sufficient foundations on engineering subjects such as science and discrete mathematics, probability/statistics; an ability to use theoretical and applied knowledge of these subjects together for engineering solutions, X
2 An ability to determine, describe, formulate and solve engineering problems; for this purpose, an ability to select and apply proper analytic and modeling methods,al background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations X
3 An ability to select and use modern techniques and tools for engineering applications; an ability to use information technologies efficiently, X
4 An ability to analyze a system, a component or a process and design a system under real limits to meet desired needs; in this direction, an ability to apply modern design methods, X
5 An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research,
6 Understanding, awareness of administration, control, development and security/reliability issues about information technologies,
7 An ability to work efficiently in multidisciplinary teams, self confidence to take responsibility,
8 An ability to present himself/herself or a problem with oral/written techniques and have efficient communication skills; know at least one extra language,
9 An awareness about importance of lifelong learning; an ability to update his/her knowledge continuously by means of following advances in science and technology,
10 Understanding, practicing of professional and ethical responsibilities, an ability to disseminate this responsibility on society,
11 An understanding of project management, workplace applications, health issues of laborers, environment and job safety; an awareness about legal consequences of engineering applications,
12 An understanding universal and local effects of engineering solutions; awareness of entrepreneurial and innovation and to have knowledge about contemporary problems.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
3. Kısa Sınav 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 4 64
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 5 5
Quiz 2 4 8
Assignment 1 10 10
Final examination 1 10 10
Total Workload 145
Total Workload / 25 (Hours) 5.8
dersAKTSKredisi 6